## Calculations For Early Start Es

In analyzing a network, the first item to be evaluated is the Early Start (ES) of each activity. This is accomplished by taking what is called a "Forward Pass" through the diagram. A "Forward Pass" is exactly what is implied. Starting with the first event or at day 0, then following the direction of the arrows and adding the durations of each activity defines the ES of the following activity. In network analysis, this number can be enclosed in a square above the Event (Node).

Figure 3-8. Network Workshop

Figure 3-8. Network Workshop

PATH

ACTIVITIES?

PATH

ACTIVITIES?

Figure 3-9. Network Workshop Solution

Figure 3-9. Network Workshop Solution

PATH

PATH

Problem 3-3: Early Start

Given the data on Figure 3-9, calculate the Early Start of each activity.

### Analysis

Working through the network it is noted that in several cases more than one activity enters a node. Since the longest path is to be determined, the largest number coming into the node should have been used in the calculation. The solution as illustrated in Figure 3-10 has a total project duration of 19 days.

CALCULATION PROCESS FOR LATE FINISH (LF)

Examination of Figure 3-10 reveals that at event 21, the Late Finish of Activities O and P has also been defined. This is a vital figure in order to calculate LF for all other activities. LF is calculated by the method known as "Backward Pass." To implement the "Backward Pass," start at the last event using the Late Finish and follow the arrows backward through the network subtracting durations to the beginning event. This then determines the LF of each activity in the network. For network analysis, this calculation will be enclosed in a circle.

Problem 3-4: Late Finish

Given the data on Figure 3-10, calculate the Late Finish of each activity.

### Analysis

Referring to Figure 3-11, working through the network again, several nodes show more than one Late Finish, since more than one activity is involved. In this case, the smaller" of the numbers will be used because the Late Finish of the subsequent node has already been established. This is easy to see at Nodes 3, 11 and 9.

Figure 3-12 summarizes the results of Figures 3-10 and 3-11, so further analysis can be made. Numbers in squares show Early Start while numbers in circles show Late Finish.

Figure 3-10. Calculation of Early Start

Figure 3-10. Calculation of Early Start

### TABULATION SOLUTION OF DATA - EF AND LS

In order to make the calculations for Early Finish (EF) and Late Start (LS) of each activity, it is easier if the data is collected in a tabular form. Figure 3-13 also gives the formulas to calculate EF and LS.

Problem 3-5: ES and LS Calculations

Given the data of Figure 3-13, calculate EF and LS.

Analysis

Figure 3-14 lists Early Finish and Late Start by activity.

### FLOAT AND ITS APPLICATION

The longest chain through the network was previously defined as the Critical Path and activities in the chain as Critical Activities. Obviously, the activities not on the Critical Path will have a certain amount of spare time by which they can be delayed and not affect

Description |
1 |
J |
DUR |
ES |
EF |
LS |
LF |
Path | ||

A |
1 |
3 |
5 |
0 |
5 |
* | ||||

B |
1 |
5 |
2 |
Q |
5 | |||||

C |
1 |
7 |
4 |
0 |
7 | |||||

D |
3 |
11 |
3 |
5 |
9 | |||||

E |
3 |
9 |
4 |
5 |
9 |
* | ||||

F |
11 |
17 |
5 |
9 |
14 |
* | ||||

G |
9 |
17 |
2 |
9 |
14 | |||||

H |
5 |
13 |
6 |
2 |
11 | |||||

J |
7 |
13 |
3 |
4 |
11 | |||||

K |
7 |
15 |
5 |
4 |
12 | |||||

L |
13 |
19 |
2 |
8 |
13 | |||||

M |
15 |
19 |
1 |
9 |
13 | |||||

N |
13 |
17 |
3 |
8 |
14 | |||||

0 |
17 |
21 |
5 |
14 |
19 |
* | ||||

P |
19 |
21 |
6 |
10 |
19 |

Calculations for each activity Forward Pass = Early Start (ES)

Backward Pass = Late Finish (LF) Early Finish (EF) = ES + Duration Late Start (LS) = LF - Duration the project completion. This spare time was defined earlier asFLOA T. Critical activities are defined as those with NO FLOAT. As also noted from the Definition exhibit, there are two types of float in a network.

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